B. Tree permutations
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

For a given tree $$$t$$$ of size $$$n$$$, a permutation of length $$$n$$$ is called $$$t$$$-good when there is an edge between nodes $$$i$$$ and $$$j$$$ if and only if there is an edge between nodes $$$p[i]$$$ and $$$p[j]$$$. For a given $$$k$$$, find a tree $$$t$$$ such that there are exactly $$$k$$$ $$$t$$$-good permutations.

Input

The first line of the input contains a single integer $$$k$$$ ($$$2 \leq k \leq 10^{18}$$$).

Output

The first line of the output should contain an integer $$$n$$$ ($$$1 \leq n \leq 400$$$)  — size of a tree or $$$-1$$$ if it does not exist.

If the tree exists, the following $$$n - 1$$$ lines each should contain two integers $$$u_i$$$ and $$$v_i$$$ ($$$1 \leq u_i, v_i \leq n$$$)  — the $$$i$$$-th edge of the tree.

Example
Input
2
Output
6
2 1
3 1
4 1
5 4
6 5